Exploring Data Visualization with Scientific Results

INTRODUCTION

DESCRIPTIVE DISTRIBUTION

An important and valuable visualization task involves representing distributions and descriptive statistics of the data. Here I will visually describe gesture production across all participants in this study.

This chart was designed as a ggplot2 object, making use of a wide range of parameters. In line with Tufte’s theory of data-ink ratio minimization, theme_light() was used to strip away the default background fill. Additional chart junk was removed as well, including all x-axis gridlines and the minor y-axis grid lines. The latter was removed in accordance with the findings of Heer and Bostock (2010) about the limits of added accuracy from gridlines. I attempted to enhance the ease of reading bars that are not directly adjacent to the gridlines by slightly reducing their opacity (alpha = .75). Tick marks were maintained along the x-axis to connect the labels with bars in an explicit way, as they do not appear to add to chart junk in a significant way while highlighting the absence of the first three bars. To develop the aesthetics of the chart, I chose a neutral but attactive hex-based color.

Note that this is a bar chart, not a histogram. It was generated with a geom_col layer. Strictly speaking, it is not a distribution, for it shows a value for each participant (proportion of trials during which they produced a gesture), whereas a histogram would instead show the distribution of gesture production as, for example, the number of trials along the x-axis (0 - 40) and the number of participants in each bin. Arguably, this chart is more informative. The order of bars was arranged in ascending order to foreground gesture production across participants, enabling comparisons comparable to those of a histogram while also showing individual level statistics. For example, we can see that all but 3 participants (87.5%) gestured on at least one trial. We also see that half of the participants gestured on more than half of the trials, and nearly half (41.7%) gestured on over two-thirds of the trials.

I make some further refinements to this chart, as follows:

For this chart, I incorporated some further design considerations. To enhance the truthfulness of the chart I relabeled the bars to correspond to participant id numbers. After all, the x-axis is a discrete, nominal variable, not to be confused with a binned continuous variable (as a histogram would show) or an ordinal variable. The ordinality here is artificial—a function of the ascending ordering of the participants by magnitude of the y value. Maintaining participant ids prevents this from being obscured. It can be misunderstood even with the explicit x-axis label by implying a false correspondence between participant number (as counted after being arranged, like in the previous chart) and the proportion of trials on which the participant gestured. There is no such correlation in the data.

I also enhanced the insightfulness of the chart with additional two elements. First, I split the groups by the variable of interest, relation type, using the color channel. This enables one to distinguish approximately how much of a given participant’s gesturing occurs in each condition. It also gives a sense of a broader pattern: that gestures are more likely to be produced on trials with the spatial relation type. The second element added to make the chart more informative is a horizontal line representing the mean proportion of trials with gesture, which allows the reader to immediately see that, on average, gestures were elicited in just over half of all trials.

In addition to the aesthetics applied in the previous chart, here I chose colors that are pleasant while discernable to the colorblind reader (based on Color Brewer pallettes). I also adjusted the font type to a serif family, based on Turfte’s claim that they are more readable (as corroborated by some results we reviewed in class).

Finally, we can add an element of interactivity to this plot, enabling further exploration with precise values for each bars segment:

COMPARING GROUP MEANS

Although descriptive, the pseudo-distributions above do not directly compare means, as is most frequently done with bar charts. *** ### BAR CHART

The typical approach to representing a inferential mean comparison results (such as ANOVA) is with a bar graph that includes standard error bars, like so:

In this chart, similar aesthetic considerations are included as the foregoing charts, but now we abandon individual-level statistics in favor of comparing the means of gesture production across our conditions of interest. This graph does show quite clearly that the means between spatial and non-spatial groups are different even when standard error is taken into account (as indicated by the error bars), although comparing these values across axes is morewhat more difficult. Comparisons are aided by the gridlines as well as inclusion of precise mean values.

• Spatial trials were more likely to elicit gesture (p = .002).

• Trial axis did not affect gesture production (p = .14).

However, by representing the means this way we lose information about the underlying distribution. This has been an increasingly common criticism of using bar plots to show mean comparisons—they may hide vastly different distributions. ⁶

The boxplot is sometimes proferred as an alternative that shows mean differences in a way that preserves information about their underlying distribution. Below is a boxplot of the same means generated with geom_boxplot. I also add a layer of points with geom_point in order to more directly show the data constituting the distribution:

While the advantage of boxplots is clear, it is also relative to the data. If the difference between means does not owe much to the difference in distributions, then bar plots seem to be adequate, although perhaps boxplots should be prefered regardless, since they would represent this fact. When it comes to the experiments with boxplots at hand, I have a couple lines of thought. First, with respect to the datapoints, it is not clear if they contribute enough to be included. Although they do show the data directly, and the clustering at the minimum and maximum values is informative, there is also the problem of overlap that suggests alternative ways to present this information may be preferable. On the ggplot2 version, I increased their size, reduced alpha to 0.75, and used jitter in order to better show the number of points in regions where there is overlap.

The second issue is that it is not clear to me how to properly translate what a traditional bar chart represents into the boxplot format. Boxplots, also known as box-and-whisker plots, typically show the median with a horizontal line, not the mean. The lower and upper edges show the 1st and 3rd quartiles, and the endpoints of the whiskers represent the minimum and maximum values. This five-point summary is useful, but it is different from the information represented by the bar chart, which shows the means and standard errors about the means. The box plot can of course be modified to convey this information: the median can be replaced with the mean, and the quartiles can be replaced with the standard errors. Yet this would also remove the distributional information that gives it comparative advantages over the bar plot. Because these representational features of the box plot are highly conventionalized, however, changing what is represented is likely to have the side effect of requiring further explanation that detracts from less contextually dependent encoding. Perhaps an alternative can be found that has the boxplot’s virtue of representing aspects of the distribution and a less context-sensitive way of representing means.

## R version 3.5.0 (2018-04-23)
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